def CremonaRichmondConfiguration():
r"""
Return the Cremona-Richmond configuration
The Cremona-Richmond configuration is a set system whose incidence graph
is equal to the
:meth:`~sage.graphs.graph_generators.GraphGenerators.TutteCoxeterGraph`. It
is a generalized quadrangle of parameters `(2,2)`.
For more information, see the
:wikipedia:`Cremona-Richmond_configuration`.
EXAMPLE::
sage: H = designs.CremonaRichmondConfiguration(); H
Incidence structure with 15 points and 15 blocks
sage: g = graphs.TutteCoxeterGraph()
sage: H.incidence_graph().is_isomorphic(g)
True
"""
from sage.graphs.generators.smallgraphs import TutteCoxeterGraph
from sage.combinat.designs.incidence_structures import IncidenceStructure
g = TutteCoxeterGraph()
H = IncidenceStructure([g.neighbors(v)
for v in g.bipartite_sets()[0]])
H.relabel()
return H
def CremonaRichmondConfiguration():
r"""
Return the Cremona-Richmond configuration
The Cremona-Richmond configuration is a set system whose incidence graph
is equal to the
:meth:`~sage.graphs.graph_generators.GraphGenerators.TutteCoxeterGraph`. It
is a generalized quadrangle of parameters `(2,2)`.
For more information, see the
:wikipedia:`Cremona-Richmond_configuration`.
EXAMPLE::
sage: H = designs.CremonaRichmondConfiguration(); H
Incidence structure with 15 points and 15 blocks
sage: g = graphs.TutteCoxeterGraph()
sage: H.incidence_graph().is_isomorphic(g)
True
"""
from sage.graphs.generators.smallgraphs import TutteCoxeterGraph
from sage.combinat.designs.incidence_structures import IncidenceStructure
g = TutteCoxeterGraph()
H = IncidenceStructure([g.neighbors(v) for v in g.bipartite_sets()[0]])
H.relabel()
return H
